If a particle had negative mass where would it go?

[Farsight]

My latex doesn't work. I think it's something to do with my Internet permissions.

And I understand negative mass as much as I understand negative colour. Which is not a lot. So if anybody could help I'd be grateful.

 

[rbj]

This would be my understanding of how it should work.

then, if you can assemble two mass of identical size but one is negative and the other positive, then you have a perpetual motion machine. patent that and you solved forever the energy resource problem of modern humanity.

still think that negative mass is for real?

 

[rbj]

Perhaps your "simple" thought is rather profound. The result of your thinking may mean the famous equation gets rewritten:

$$E = m(\pm c^2)$$

Just my simple thought

i s'pose you're being facetious. (i can't always tell.)

 

[WhyIsItSo]

i s'pose you're being facetious. (i can't always tell.)

Me either

 

[NoTime]

then, if you can assemble two mass of identical size but one is negative and the other positive, then you have a perpetual motion machine. patent that and you solved forever the energy resource problem of modern humanity.

still think that negative mass is for real?

You might have noticed that I cut that part from your original post.
For perfectly matched masses, nothing will happen.
The attraction of one would balance the repulsion of the other. Net effect is 0.

I'll wait to when (or if) they can get anti H to form and can run an experiment with it.
Until then this is just speculation.

Edit: Just a clarification. The concept that one mass would run away from the other is based on negative mass also having negative inertia. I don't see an absolute reason why this should be so.

 

[WhyIsItSo]

Not wanting rbj to think I am always facetious, here is my serious thinking.

Premise​

All mass is a postive measure, or perhaps mathematically more accurate would be to say it is an unsigned value. All matter, whether normal, negative, or anti, has inertia. It takes some force to accelerate it. Therefore it has mass, and that is mathematically taken as a positive value.

Arguments Supporting Premise​

Whether matter is normal-, negative-, or anti-matter, it requires some force to accelerate it. To illustrate that mass cannot be viewed as a negative quantity, consider:

We use $$F=ma$$ to express force. Hypothesizing that, for example, negative mass might be repelled by forces that would attract normal mass has no bearing. This merely reverses the vector of the Force. In a free body diagram, you would reverse the arrow. If you arbitrarily chose to instead reverse the sign of F, then you have reversed the sign of acceleration, ie., $$-F=m(-a)$$. The "positive" or "negative" respresentation has no bearing on mass. Mass is a magnitude only.

Also, again since all matter has inertia, it therefore has mass. No matter how small the magnitude, some force is required to accelerate it. Only by converting mass to energy can you remove this value.

Therefore, $$m>0$$ is always true, since it must be represented mathematically as a positive value, and to be 0 it must be converted to energy, hence is no longer matter.

$$E=mc^2$$ is safe. It is not contradicted by, nor is there any conondrum because of the concept of negative-matter. Since $$c^2$$ is decidedly postive, and m is shown to be positive, E is therefore always positive, as it must be. For similar logical reasons, E is a magnitude/rate, but has no vector. It is meaningless to apply a sign to this value. Do not confuse this with a rate of change, which would introduce a sign, since it now has a vector (we must note the direction of change).

Next I will debunk any perpetual motion hpothesis.

 

[WhyIsItSo]

The hypothesis from some has been that perpetual motion may be possible with negative matter.

Premise​

1. Perpetual motion is impossible. Specifically, the arguments in this thread on the subject are both in violation of logic, and are fundamentally flawed in their premise regarding behavior.

2. Normal Matter and Negative matter will attract on the macroscopic level (ie, gravity). I make no prediction at for quantum level, but will show this is irrelevant to the issue of perpetual motion.

Arguments Supporting Premise​

Argument 1
To produce a perpetual motion machine, some sustained net force is required. This has variously been argued by suggested differences in how negative matter would respond to normal matter, and comparing that to how normal matter would respond to negative matter.

Seperating these behaviors is necessarily a gross error in logic. Whatever the natures of the two types of matter, they wll either attract, or repel. There will be some net force that acts upon this system, and the system will move towards equilibrium.

Have you ever encountered the story of 3 brothers who bought a radio? The radio they want costs $30. They put in $10 each, and give it to a young lad to run to town and buy the radio. The store owner decides to give the brothers a $5 discount, so the lad returns with the radio and $5. Along the way, he realizes he can't readily divide 5 by 3, so when he gets back, he gives each brother $1, and keeps $2 for himself. This now means each brother paid $9. $9 x 3 = $27, and the boy has $2. $27 + $2 equals $29. Where is the missing $1?

Such is the nature of the above perpetual argument. It is pure and simply a mixing of two unrelated equations in such a manner as to make them appear related.

Argument 2
What about the question of whether or not the type of matter will attract or repel? I assert they will attract macroscopically, that is, gravitationally speaking.

First, recall that many "wrong" ideas can still be used in everyday context. A centrifuge works on the "idea" of centrifugal force. Though we know there is no such force, it is often convenient to overlook that fact. How about weight? Because we mostly use this on the face of this planet, we freely exchange the terms weight with mass. But mass has no vector, weight does. They do not even have the same units of measure. Remember that weight is really mass times g, and g is the "downward" accleration we take as 9.8m/s^2. Most of the time, we can get away with ignoring this fact, but when delving into issues where this matters, we must return to more formal concepts.

In like manner, we must remember here that treating gravity as a force is convenient, but not accurate. I would be interested to know if anyone can offer any other "force" that we cannot feel unless there is some opposing force. Please omit any forces that, due to their magnitude, are impercetable to us. Gravity is decidedly strong enough that we feel its effects, but only while some force opposes it, and only to the magnitude of that opposing force. Logically, therefore, while standing on the ground, the only force you feel is the ground accelerating you in an "upwards" direction at 9.8m/s^2 or thereabouts. We hold a concept that the peculiar nature of gravity is such that it affects all parts of our body simultaneously, whilst the ground presses back at only the contact area of our feet.

If gravity is not a force, then we must throw out the Newtonian concept that for every force there is an equal an opposite force, otherwise we would be launched skywards. Yet we remain firmly planted on the ground. So there must be a force to balance... and around we go to conclude gravity is a force.

Just like we conclude that a centrifuge operates by centrifugal force, until our understanding reveals the truth.

I do not profess to know the explanation for space-time bending due to a mass, but this concept can be used to satisfy the apparent contradiction above.

If you accept that, then consider this. If gravity is not a force, I suggest it has no vector. Where I traveling in space and approaching the gravity well of Earth closely enough to be "attracted" to it, I will feel no acceleration; because there isn't any. From my perspective, I continue to travel in a straight line, at a constant speed. My velocity does not change. Hence, if my path nevertheless "seems" to deviate towards Earth, then it must follow that the light reaching my eyes is not as affected by the bending as is my body. Since mass is a magnitude only, this bending is a magnitude only, and its magnitude is a function of the magnitude of the mass causing it. In this scenario, the Earth's mass is constant, so the difference I perceive is between the mass of the light, and my mass. I too am bending space-time, just not very much compared to the Earth. Better to say, I probably am bending it just as much, just in a much smaller region; a smaller scale if you will. I suspect "mapping" this bending would not be entirely disimilar to how we represent magnetic fields. Not the same, but there would be "curves" which "tighten" in close proximity to the mass.

That is conjecture on my part. What matters is that the bending of space-time is a magnitude only. There is no "negative bending" is you will.

Therefore, negative matter, having mass (which is a positive value), will also bend space-time around itself.

More important to this discussion, there is no acceleration involved. Hence, there is no force involved. Hence, any consideration of repulsion or attraction (being necessarily vectors) is irrelevant. The Earth is bending space-time, so all matter, having inertia, will continue on in the direction, and with the speed, it started with, but this "straight line" is altered by the gravity well of Earth, so the negative matter will "fall" towards Earth.

Note that the gravity well of Earth has nothing to do with a reaction on the negative matter. It is a phenomenon of space-time. Space-time is bent, and that's that. Matter, of any form, will simply follow its "straight" path along this well. The only thing that affects the actual path is the mass of the matter; how much is it bending space time?

The interactions, therefore, are expressed only in terms of the magnitude of space-time bending; there is no issue of "sign". From the perspective of an observer (whose perceptions are based on light, and the path that takes), will simply be that the greater mass has the greater influence. Observing our moon in orbit, the observer may notice that the Earth appears to wobble as a result of the Moon's influence. But remember that the visual perception (light-based) and the actual event (dependent on the mass of the objects observed) will not be the same, because light is not nearly as affected by a gravity well as, for example, something with as much density of mass as the Moon or Earth.

Finally, and briefly, there is the level at which issues such as electrostatic forces and whatnot become significant. Please don't get bent out of shape by my clumsy naming or lack of understanding of such issues. Detailed knowledge of such may be required to calculate net forces, but one need not be a quantum physicist in order to predict there will be some net force. Why normal matter and negative matter might attract or repel, is not at issue. That they will do one or the other, and that will result in some net force, which will move towards equilibrium, is all that is important to this discussion.

Unfortunately for those hoping for a perpetual motion device, "equilibrium" negates such a possibility.

 

[NoTime]

Premise​

All mass is a postive measure, or perhaps mathematically more accurate would be to say it is an unsigned value. All matter, whether normal, negative, or anti, has inertia. It takes some force to accelerate it. Therefore it has mass, and that is mathematically taken as a positive value.

Mass has two properties.
One is inertia the other is spacetime curvature otherwise known as gravity.
Generally the only way we have of measuring mass is by measuring its inertia.
Its easy enough to imagine that the curvature of antimatter could be opposite that of normal matter and still have positive inertia.

So a small amount of antimatter might still "fall down"
as it is constrained to follow the geodesic set by a large amount of normal matter.
OTOH two masses of antimatter would repel each other.

AFAIK there is no way to eliminate this possibility short of doing an Etovos experiment with antimatter.

 

[Andrew Mason]

We use $$F=ma$$ to express force. Hypothesizing that, for example, negative mass might be repelled by forces that would attract normal mass has no bearing. This merely reverses the vector of the Force. In a free body diagram, you would reverse the arrow. If you arbitrarily chose to instead reverse the sign of F, then you have reversed the sign of acceleration, ie., $$-F=m(-a)$$. The "positive" or "negative" respresentation has no bearing on mass. Mass is a magnitude only.

But the distinctive quality of negative mass, if it exists, is that it accelerates in the opposite direction to force:

$$F \propto -a$$ so:

$$-F = ma \ne m(-a)$$

You cannot use logic to eliminate the possibility of negative mass. You need evidence.

AM

 

[WhyIsItSo]

Mass has two properties.
One is inertia the other is spacetime curvature otherwise known as gravity.
Generally the only way we have of measuring mass is by measuring its inertia.
Its easy enough to imagine that the curvature of antimatter could be opposite (1)that of normal matter and still have positive inertia.

So a small amount of antimatter might still "fall down"
as it is constrained to follow the geodesic set by a large amount of normal matter.
(2)OTOH two masses of antimatter would repel each other.

AFAIK there is no way to eliminate this possibility short of doing an Etovos experiment with antimatter.

1. For that to hold, you must show mass as having a negative value. So you need to argue against my reasoning for stating mass is also a positive. I am curious to see what you offer.

2. Since the context is space-time bending, this statement is also dependent on (1).

An important tenet of my argument is that gravity is not a force, yet it appears to me your concept remains embedded in notions of vector. My explanation of space-time is such that no acceleration occurs, therefore the path an object takes in the presence of gravity has no direct connection with inertia.

Since there is a relationship between gravity and mass, and there is a relationship between mass and inertia, it seems logical that a relationship between gravity and inertia could be expressed.

But keep in mind that inertia has a vector (possibly undefined as 0), whilst gravity and mass do not. Also, a 0 inertia vector is a relative concept. To an object itself, it's inertia vecotr is 0, it can consider itself stationary, and all observed motion means those objects are moving. But to one of those "moving" objects, the original observer is moving, hence it has some vector to its inertia. We are dealing with issues of relativity, so you must be careful how you form your concepts

 

[WhyIsItSo]

But the distinctive quality of negative mass, if it exists, is that (1)it accelerates in the opposite direction to force:

$$F \propto -a$$ so:

(2)$$-F = ma \ne m(-a)$$

You cannot use logic to eliminate the possibility of negative mass. (3)You need evidence.

AM

I would answer your statement (1) with your own assertion (3).

2. That is not the equation I presented. Neither, at any point, did I attempt to "eliminate the possibility of negative mass".

 

[blackwizard]

Just a simple suggestion. I heard tachyons, negative mass, are supposed 2 travel backward in time. If that meant that some of the logic used here would have 2b completely reversed if ye were assumin they travel in the normal time direction. Like it repeling a positive mass (backward in time) but when viewed by us it would look like its attracting it, like all other mass?

 

[Andrew Mason]

That is not the equation I presented. Neither, at any point, did I attempt to "eliminate the possibility of negative mass".

I guess I misunderstood your statement:

Therefore, m > 0 is always true,

AM

 

[rbj]

But the distinctive quality of negative mass, if it exists, is that it accelerates in the opposite direction to force:

$$F \propto -a$$ so:

$$-F = ma \ne m(-a)$$

did you not mean:

$$F = ma \ne m(-a)$$

or more specifically

$$\vec{F} = \frac{d \vec{p}}{dt} = m \vec{a}$$

if we can assume the mass is constant.

You cannot use logic to eliminate the possibility of negative mass. You need evidence.

can we use logic to eliminate the possibility of a perpetual motion machine? if not, what evidence is sufficient? we can't look everywhere in the universe to verify that no perpetual motion machine lives there.

i think we can use existing knowledge of physical behavior, analytical extension of that physical behavior (with the minus signs), and logic to conclude that two balls of mass with equal magnitude and opposite sign makes a system that accelerates indefinitely.

i've seen some posters here deny that, but they are not saying why.

 

[rbj]

So a small amount of antimatter might still "fall down"
as it is constrained to follow the geodesic set by a large amount of normal matter.
OTOH two masses of antimatter would repel each other.

AFAIK there is no way to eliminate this possibility short of doing an Etovos experiment with antimatter.

this is not about antimatter. it's about negative mass and, as best as i can read about it, the two are different.

is not "antimatter" this stuff where electrons are replaced by positron and protons are replaced by antiprotons? i just looked these two antiparticles up and they believed to have positive mass. antiparticles have the same (positive) mass as their normal counterparts and the opposite electric charge.

if there was no gravity, the motion of such might be indistiguishable from having the same electric charge and opposite mass (in an electrostatic context, the particle motion would be the same).

but this thread is about negative mass and its motion in the context of gravity. and that's where you can tell the difference.

negative mass means perpetual motion machines, the end of conservation of energy, and the solution to humankind's energy shortage forever.

so may i suggest that we don't use the term "antimatter" to mean matter with negative mass?

and may i suggest to those who say that equal and oppositely massed objects (also uncharged, electrically) will either just attract each other or just repel each other (because of gravity), to show what the justification they have for such a belief?

 

[NoTime]

1. For that to hold, you must show mass as having a negative value. So you need to argue against my reasoning for stating mass is also a positive. I am curious to see what you offer.

Since it is currently not possible to run an Etovos experiment with antimatter, I'm kind of curious as to how you would expect me to do this.

An Etovos experiment is the only way I know of to measure the "force" of gravity directly as opposed to simply measuring inertia.

While it seems that they have created anti-H, the mean lifetime is currently around 10^-9 sec. Not long enough to be meaningful. Plus I suspect they'd have to at least get to anti-H_2, so van der wals forces didn't swamp any possible data.

There are many ways to set up math to play with this.
That different ways seem to be mathematically valid, while giving different results, says to me that we have to wait for a defining experiment.

 

[NoTime]

this is not about antimatter. it's about negative mass and, as best as i can read about it, the two are different.

This probably says it better than I can
http://en.wikipedia.org/wiki/Negative_mass#Negative_mass

 

[Hurkyl]

if there was no gravity, the motion of such might be indistiguishable from having the same electric charge and opposite mass (in an electrostatic context, the particle motion would be the same).

They're still distinguishable -- look at the electric field they generate. They have opposite charge if and only if they generate opposite fields.

 

[WhyIsItSo]

I guess I misunderstood your statement:

AM

...Which was $$m>0$$.

My apologies, I stand corrected. What I was thinking was that I am not challenging negative matter. You are correct, however, that I do challenge negative mass.

Ergo, I assert that negative matter, if it exists, has positive mass.

 

[WhyIsItSo]

Just a simple suggestion. I heard tachyons, negative mass, are supposed 2 travel backward in time. If that meant that some of the logic used here would have 2b completely reversed if ye were assumin they travel in the normal time direction. Like it repeling a positive mass (backward in time) but when viewed by us it would look like its attracting it, like all other mass?

[facetious]
Perhaps, since they are purported to travel backwards in time, then their behavior could be described as simply as recording the life and path of a photon, then playing the film backwards.
[/facetious]

 

[WhyIsItSo]

You cannot use logic to eliminate the possibility of negative mass. You need evidence.

can we use logic to eliminate the possibility of a perpetual motion machine? if not, what evidence is sufficient? we can't look everywhere in the universe to verify that no perpetual motion machine lives there.

i think we can use existing knowledge of physical behavior, analytical extension of that physical behavior (with the minus signs), and logic to conclude that two balls of mass with equal magnitude and opposite sign makes a system that accelerates indefinitely.

i've seen some posters here deny that, but they are not saying why.

Thank you.

 

[WhyIsItSo]

and may i suggest to those who say that equal and oppositely massed objects (also uncharged, electrically) will either just attract each other or just repel each other (because of gravity), to show what the justification they have for such a belief?

Hmmm, sounds like I may be included in "those".

For my part, my guess is that, for any two particles, there will be either an attraction or a repulsion when in close enough proximity for such atomic-level forces to be meaningful. Again, forgive my ignorance of the correct terms here; I trust you understand what I mean.

My assertion thus far has been, gravitationally, issues of "repel or attract" are not applicable. Such issues imply acceleration, and none occurs.

 

[WhyIsItSo]

1. For that to hold, you must show mass as having a negative value. So you need to argue against my reasoning for stating mass is also a positive. I am curious to see what you offer.

Since it is currently not possible to run an Etovos experiment with antimatter, I'm kind of curious as to how you would expect me to do this.
<snip>

I am not asking for experimental evidence. My opinions are not carved in stone; I am not dogmatic about this issue. But since you cannot perform this Etovos experiment, using that specifically as an example hardly constitutes an argument, does it?

If you have some sound logic, however, to dispute my logic, I'm ready to listen - seriously. If there is a flaw in my reasoning, I'd prefer to be mildly embarrassed now than walk around for the next n years thinking something that is foolish.

 

[rbj]

They're still distinguishable -- look at the electric field they generate. They have opposite charge if and only if they generate opposite fields.

i just don't know fundamentally how to test an E field without plopping in a test charge and watching it go somewhere. wouldn't a negative mass test charge move the same way as if it were positive mass with opposite charge?

and test charges are so small that the E field that they generate is much, much smaller than the E field that they're measuring.

 

[rbj]

Hmmm, sounds like I may be included in "those".

For my part, my guess is that, for any two particles, there will be either an attraction or a repulsion when in close enough proximity for such atomic-level forces to be meaningful. Again, forgive my ignorance of the correct terms here; I trust you understand what I mean.

My assertion thus far has been, gravitationally, issues of "repel or attract" are not applicable. Such issues imply acceleration, and none occurs.

but that is not correct. two neutrally charged masses, one of +M, the other of -M will accelerate, but they will accelerate in the same direction. the -M mass will acclerate toward the +M mass and the +M mass will accelerate away from the -M mass.

 

[Hurkyl]

i just don't know fundamentally how to test an E field without plopping in a test charge and watching it go somewhere. wouldn't a negative mass test charge move the same way as if it were positive mass with opposite charge?

Use the same test charge for both!

Put an electron next to an electron. Which way does the electron go?
Put an electron next to a positron. Which way does the electron go?

Those answers will be the same if and only if the electron and positrion have the same charge, no matter what their masses are.


Oh, here's another one. Place two identical charged particles next to each other. They repel each other if and only if their mass has the same sign as the k in kqQ/r^2.

 

[NoTime]

I am not asking for experimental evidence. My opinions are not carved in stone; I am not dogmatic about this issue. But since you cannot perform this Etovos experiment, using that specifically as an example hardly constitutes an argument, does it?

If you have some sound logic, however, to dispute my logic, I'm ready to listen - seriously. If there is a flaw in my reasoning, I'd prefer to be mildly embarrassed now than walk around for the next n years thinking something that is foolish.

I guess I didn't make myself clear.
It isn't currently possible to prove this by logic or math.

Perhaps someone might come up with a good idea that would allow us to discriminate between the various possibilities.
Which is likely why this thread isn't locked already.

As to your exact argument, other people have pointed out some items.

Personally I don't see anything wrong with being foolish as long as you are paying attention to what may or not may not be allowed.
Some of my best ideas have been destroyed by ugly reality.

 

[NoTime]

but that is not correct. two neutrally charged masses, one of +M, the other of -M will accelerate, but they will accelerate in the same direction. the -M mass will acclerate toward the +M mass and the +M mass will accelerate away from the -M mass.

Only if you flip the sign of curvature AND the sign of inertia. It isn't clear to me that this is necessary.

 

[rbj]

Only if you flip the sign of curvature AND the sign of inertia. It isn't clear to me that this is necessary.

we don't decide what is necessary or not, nature does. you have to show what reason you would not flip the signs in any case of negative mass. why would nature bother to essentially apply an absolute value operator to any of the three types of masses (that the Equivalence Principle says is one-and-the-same)?

negative intertial mass means the object moves in the opposite direction that it is pushed. negative passive gravitational mass means that the object in a regular gravitational field (from a much larger planet of positive mass) will have an upward force. so if both inertial mass and passive gravitational mass is the same mass, the two minus signs cancel and the small negative mass still falls toward the planet. from a GR perspective, this is consistent, because the curvature is determined by the much larger planet mass which is positive, in this case. the geodesic path is the same no matter what the quantitative value of the test mass is (as long as it's small and not contributing significantly to the curvature), whether it is positive or negative.

now consider a small test mass with positive mass and a big planet of negative mass. does that test mass fall toward the planet or get repelled away? does the curvature (when translated to flat Euclidian space) curve in toward the planet of large negative mass or away from it?

once you answer that, tie together all of the concepts and ask what happens when you have two planets of opposite signed mass and equal magnitude separated by some distance. what are the geodesic paths like that are created by the negative mass and in the vicinity of the positive mass? and vice versa? that's when you get a nice accelerating (from the POV of Newtonian 3-space) pair of planets that will accelerate indefinitely.

 

[rbj]

Use the same test charge for both!

Put an electron next to an electron. Which way does the electron go?
Put an electron next to a positron. Which way does the electron go?

Those answers will be the same if and only if the electron and positrion have the same charge, no matter what their masses are.


Oh, here's another one. Place two identical charged particles next to each other. They repel each other if and only if their mass has the same sign as the k in kqQ/r^2.

Hurkyl, I'm with you.

i was thinking about the test charge being the one with possible negative mass and the charge setting up the field being constant.

i think we're on the same page, at least now.

 

[NoTime]

once you answer that, tie together all of the concepts and ask what happens when you have two planets of opposite signed mass and equal magnitude separated by some distance. what are the geodesic paths like that are created by the negative mass and in the vicinity of the positive mass? and vice versa? that's when you get a nice accelerating (from the POV of Newtonian 3-space) pair of planets that will accelerate indefinitely.

Far be it from me to complain that Forward has his math wrong.
OTOH, ignoring any QFT, in GR gravity isn't a force. It's a condition of space.
What force is pushing against the -inertia to make it push back?

we don't decide what is necessary or not, nature does.

Exactly. And this is one of the things where nature hasn't divulged her secrets.

you have to show what reason you would not flip the signs in any case of negative mass. why would nature bother to essentially apply an absolute value operator to any of the three types of masses (that the Equivalence Principle says is one-and-the-same)?

I think that might be more like "observed to be the same".

The only way we know energy is thru photons.
Photons exhibit no net space-time curvature.
However, photons are considered to have momentum, a vector quantity.
If you bounce a bunch of photons off something it will move, as shown by experiment.
Now if you toss -e at +e and they annihilate, you might think everything would vanish.
They are after all anti-particles.
However, two 511mev photons are generated traveling in opposite directions.

Is +Energy and -Energy already absolute?
Only the relative direction the momentum vector points in designates the sign?
In any event you seem to end up with two electrons worth of momentum.
If energy is absolute then inertia needs to be as well to satisfy E=MC^2.
Can you have |+- curvature| = inertia?

 

[rbj]

Far be it from me to complain that Forward has his math wrong.
OTOH, ignoring any QFT, in GR gravity isn't a force. It's a condition of space.
What force is pushing against the -inertia to make it push back?

i think that gets answered when you come to the conclusion that there ain't no negative mass. (this is why i said it leads to contradiction.)

The only way we know energy is thru photons.
Photons exhibit no net space-time curvature.
However, photons are considered to have momentum, a vector quantity.
If you bounce a bunch of photons off something it will move, as shown by experiment.
Now if you toss -e at +e and they annihilate, you might think everything would vanish.
They are after all anti-particles.
However, two 511mev photons are generated traveling in opposite directions.

Is +Energy and -Energy already absolute?
Only the relative direction the momentum vector points in designates the sign?
In any event you seem to end up with two electrons worth of momentum.
If energy is absolute then inertia needs to be as well to satisfy E=MC^2.
Can you have |+- curvature| = inertia?

dunno why all of this is germane. i would still suggest taking it up with John Baez (that sci.physics.research post i cited earlier). in GR, gravity is not a force, but when spacetime is flat enough and speeds are slow enough, the Newtonian model in 3-space is a very good approximation and it's easier to look at intuitively when you look at it. you count the minus signs and a negative mass repels anything while a positive mass attracts anything. two equal sized and opposite masses will result in one always attracting the other, while that other always repels the first.

 

[Hurkyl]

Photons exhibit no net space-time curvature.

Photons have energy and momentum. Energy and momentum contribute to the stress-energy tensor. The stress-energy tensor affects controls how space-time is curved.

So yes, photons do curve space-time.

Now if you toss -e at +e and they annihilate, you might think everything would vanish.

An alternative is to create a pair of photons traveling opposite directions through time as well as space.

Hrm... I'll have to mull over what the consequences of that are!

 

[NoTime]

Photons have energy and momentum. Energy and momentum contribute to the stress-energy tensor. The stress-energy tensor affects controls how space-time is curved.

So yes, photons do curve space-time.

I tried to get away from that by saying net.
If they had a net curvature then wouldn't a photon have mass?
I do think they curve space-time, but with equal amonts of positive and negative curvature.
Thus, no mass.

I'm no GR expert, but at one time I could stumble through MTW. Doubt I could still do the math or at least not without a tremendous amount of rework.

An alternative is to create a pair of photons traveling opposite directions through time as well as space.

Hrm... I'll have to mull over what the consequences of that are!

They do!
But time isn't anything like whatever you think it might be.

 

[rbj]

...Thus, no mass.

this is a good reason for why i think that physics curriculums have made a pedgagical mistake in the last 2 decades by deciding to ignore the differentiation between rest mass (or "invariant mass") and relativistic mass.

photons have mass:

$$m = \frac{E}{c^2} = \frac{h \nu}{c^2}$$

this mass causes the same amount of curvature in space-time as would any other mass of the same quantity (but sometimes that is represented as energy density divided by $c^2$).

however, the rest mass

$$m_0 = m \sqrt{1 - \frac{v^2}{c^2}}$$

is zero because $v = c$.

Photons have mass, but no rest mass.

you've also done nothing to support your use of an absolute value function to apply to either gravitational mass or inertial mass. the reality of negative mass leads to perpertual motion machine and the obsolesence of the conservation of energy.